Question 259757
Instead of subscript 1 and 2, let's do this
{{{x1=x}}}
{{{x2=y}}}
It'll reduce the confusion, I think. 
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1.{{{x-5y=1}}}
2.{{{3x-7y=5}}}
Use eq. 1 to solve for x in terms of y. 
{{{x=1+5y}}}
Now substitute into eq. 2 and solve for y.
{{{3x-7y=5}}}
{{{3(1+5y)-7y=5}}}
{{{3+15y-7y=5}}}
{{{8y=2}}}
{{{y=1/4}}}
Then use eq. 1 again,
{{{x=1+5y}}}
{{{x=1+5(1/4)}}}
{{{x=9/4}}}
Now we can re-name them back to the originals,
{{{x1=9/4}}}
{{{x2=1/4}}}